The broad, long-term objectives of this research are the developments of innovative and high-impact statistical methods for the designs and analysis of chronic disease studies, with an emphasis on genomics. The specific aims of this competing renewal application include: (1) efficient estimation for general two-phase studies, in which possibly incomplete multivariate outcomes and inexpensive covariates are measured on all study subjects in the first phase and the first-phase information is used to optimally select subjects for measurements of expensive covariates in the second phase; (2) valid and efficient analysis of genetic association when all study subjects are genotyped on a SNP array but only a small subset is sequenced or when unobserved allele-specific copy numbers are of direct interest; (3) meta-analysis under random-effects models when the number of studies is small relative to study sample sizes and variable selection based on summary statistics of multiple studies under a variety of model structures. All these problems are motivated by the principal investigator's applied research experiences and are highly relevant to current genomic studies. The proposed solutions are based on likelihood and other sound statistical principles. The large-sample properties of the new methods will be established rigorously via modern empirical process theory and semiparametric efficiency theory. Efficient and stable numerical algorithms will be developed to implement the inference procedures. The proposed methods will be evaluated extensively through simulation studies mimicking real data and be applied to several major genomic studies, most of which are carried out at the UNC. Efficient, reliable and user-friendly software with proper documentation will be freely available. This research will not only advance the fields of biostatistics and statistical genetics but also influence chronic disease research at the UNC and elsewhere.